Some results on almost Kenmotsu manifolds

Abstract

First we consider almost Kenmotsu manifolds which satisfy Codazzi condition for and , and we prove that in such cases the tensor vanishes. Next, we prove that an almost Kenmotsu manifold having constant -sectional curvature which is locally symmetric is a Kenmotsu manifold of constant curvature . We also prove that, for a -almost Kenmotsu manifold of with , every conformal vector field is Killing. Finally, we prove that if is a -almost Kenmotsu manifold with and , then the vector field which leaves the curvature tensor invariant is Killing.